In a triangle with side lengths 5, 6 and x, what is the sum of all possible integral values of x?

We have that

x < 5 + 6 and 5 + x > 6

x < 11 x > 1

So, Logic.....just sum the integers 2 through 10 and there's your answer....!!!!

Right, gives 10*11=110/2=55-1=54.