Where are the add-ons in Skyrim Legendary Edition?

So I bought Skyrim Legendary Edition for PC (specifically the entire Elder Scrolls Anthology collection) and I already had the plain version of Skyrim on my computer. What I did was uninstall the original version of the game, which left it in my Steam profile, even though it was inaccessible. I used the Legendary Edition disc and reinstalled the game using that. After downloading this version, the Skyrim file in Steam reinstalled, but it started from about 80%, kind of as if it had everything it needed but the new files from the DLC. When I restarted the game, the DLC wasn't listed under data files (in fact, nothing is there) and upon playing the game, I found that everything was as I left it. The add ons didn't seem to have done anything. Saves, mods and all were in tact, albeit with all my settings reset. So before I go through all kinds of hassle, do I have to restart the game on a different file for it to all work? Is there something I have to find in the game files in order to do all this? Any clarification would help.