Is there any answer that is not logically/sensibly disputable?

No there is not. For as long as you study philosophy or any other subject, there will always be one word that makes everything a theory. WHY? No matter what answer you give one can always ask WHY? to dispute it. This will go on until one cant answer the question why anymore.

An answer that is disputable is part of the Logos. This includes scientific inquiry and political debate.

An answer that is not disputable is part of the Mythos. The mythos is something you just believe, you can't be talked out of it. Some examples of the American mythos includes: All people are created equal. People have certain inalienable rights such as life and liberty. If somebody disagrees with these points, they disagree. To most Americans, they are not up for dispute.

A yes or no answer.

Do you want cake? No. What dispute is there in that answer. I do not want cake.

yes

yes, we called it "deciding the answer with a coin toss"

That what we call penis and what we call vagina work in symbiotic relations toward the same goal.....

yes, there is.