We have the equation 11^(5x-6)=1/11^(-x-10) to solve for x.

11^(5x-6)=1/11^(-x-10)

=> 11^(5x - 6) = 11^[-( - x - 10)]

=> 11^(5x - 6) = 11^(x + 10)

as the base is the same we can equate the exponent.

5x - 6 = x + 10

=> 5x - x = 10 +6

=> 4x = 16

=> x = 16/4

=> x = 4

**Therefore x = 4**