MathNet 2014 Question 100

Suppose that the function $y = f(x)$ satisfies $1 - y = \frac{9 e^{x} + 2}{12 e^{x} + 3}$. If $m$ and $n$ are consecutive integers so that $m \lt \frac{1}{y} \lt n$ for all real $x$, find the value of $mn$.