how to find integer solutions of algebra problem involving division and powers

Question

$x = (3^n - 2^n) / (2^{m+n} - 3^n)$

$n$, $m$, and $x$ must be positive integers $\geq 1$

$x$ must also be odd

The trivial solution is

$n=1, m=1, x=1$

Are there any other solutions? If not, is there a way to prove there are no other solutions?