Answer
$f^{-1}(x)=\frac{-6x-5}{1-x}$
Work Step by Step
I can find the inverse function by "swapping" $x$ and $f(x)$ and then solving the equation for $f^{-1}(x)$:
$x=\frac{f^{-1}(x)+5}{f^{-1}(x)-6}\\x(f^{-1}(x)-6)=f^{-1}(x)+5\\-6x-5=f^{-1}(x)(1-x)\\f^{-1}(x)=\frac{-6x-5}{1-x}$
