In the Hebrew language what is it that determines whether "בָּרַךְ bârak" is "bless" or "curse"?

The Hebrew doesn't say "Barak" in Job 9:11 to mean blessed. In verse 11 the Hebrew is "Yevarekeka". In verse 10 previous to it, "Berachta" 'have blessed' literally means God has blessed the work of Job's hands. In neither verse 9-11 is the word Barak used to curse. 

In the second verses 20-21 the word "mevorak" also can be pronounced "meborak". Which means may God's Name be praised or blessed in prayer. 

There are actually examples in the bible where e.g. Job 2:9 and 1Kgs 21:10, 13 used the word in Hebrew "Barek" is used as euphemism to mean curse. The reason this is done is because we never in scripture want people to say "cursed - IS then insert God's Name heaven forbid! The context or interpretation could unintentionally be used to curse God. We revere God so much that we don't even want to put cursed next to God's Holy Name. 

The actual Hebrew terminology we use is Chillul Hashem meaning God's Name has been profaned. The word Chillul means to invoke or misuse something which is holy or could be made holy i.e. elevated through our divine service and Hashem means God's Name. Why doesn't scripture just say Chillul Hashem? Because it can also mean to do an action which brings God's Name into reproach. Any action that brings God's reputation in repute is desecrating God's Holy Name. Ask a JW for example what does it mean to bring God's Name into reproach? They will most likely say using God's Name in an unworthy manner or an action which so-to-speak embarrasses God. 

The scripture wants to be dead accurate what the person did in the bible. The person didn't do an action unintentionally to bring God's Name into the mud, no! He actually cursed God's Name i.e. blasphemy. 

1288 barak baw-rak' a primitive root; to kneel; by implication to bless God (as an act of adoration), and (vice-versa) man (as a benefit); also (by euphemism) to curse (God or the king, as treason):--X abundantly, X altogether, X at all, blaspheme, bless, congratulate, curse, X greatly, X indeed, kneel (down), praise, salute, X still, thank.

 - the answer is context. (to kneel)

          in adoration. (to bless)

but.....

also (by euphemism)  = curse 

Thanks for the question and the answer, I don't know Hebrew and have never read the Hebrew Bible but I learned something new today.

Hebrew is a very picturesque language. The word בָּרַךְ bârak actually means to break down and fall to one's knees for any reason. The two primary reasons are to lament in grief and to rejoice. Either way, it implies being so overwhelmed with emotion that we emote something automatically from deep within us, revealing our real feelings and beliefs. This can be either cursing or blessing, both of which occur only afterwards, not during בָּרַךְ bârak. Why we are overwhelmed with emotion is revealed by what happens next. 

In the sense that GOD 'blesses' or 'curses' He may not be overwhelmed like a man, but He Is still emoting His true feelings about something and speaking without reservation about something or someone's blessing or destruction. This comes over Him just as suddenly and the blessing or curse arrives afterwards. 

"Trust in the LORD with all thine heart; and lean not unto thine own [Hebrew and Greek languages included] understanding" (Proverbs 3:5).