jmc

Let $y=\frac{2x+5}{x-11}.$ Then $$xy-11y=2x+5,$$so $xy-2x=11y+5.$ Then $x=\frac{11y+5}{y-2}.$

Hence, the inverse function is given by $$f^{-1}(x)=\boxed{\frac{11x+5}{x-2}}.$$