To solve this equation, we can start by finding a common denominator.

Multiplying both sides of the equation by (x - 11)(x - 15), we get:

15(x - 15) = 11(x - 11)

Expanding both sides, we get:

15x - 225 = 11x - 121

Next, we can simplify the equation by combining like terms:

15x - 11x = 225 - 121

4x = 104

Finally, divide both sides by 4 to solve for x:

x = 26

Therefore, the solution to the equation is x = 26.