Getting a common denominator on the left, we have
(11/30)x = 11/6 ..... and 11/6 = 55/30 .....so we have...
(11/30)x = (55/30) and since the denominators are the same, we can solve for the numerators
11x = 55 divide both sides by 11
x = 5
I do it a little differently
x/6+X/5=11/6
the lowest common denominator is 5*6=30
So I would strat bey multiplying both sides by 30 to get rid of the fractions.
30(x/6+x/5)=30*11/6
5x+6x=55
11x=55
x=11