Do there exist natural numbers $m$ and $n$ for which the equality is true: $\left(-2 a^{n} b^{n}\right)^{m}+\left(3 a^{m} b^{m}\right)^{n}=a^{6} b^{6}$?
Indeed, for $m=3, n=2,\left(-2 a^{n} b^{n}\right)^{m}+\left(3 a^{m} b^{m}\right)^{n}+\left(-2 a^{2} b^{2}\right)^{3}+\left(3 a^{3} b^{3}\right)^{2}=-8 a^{6} b^{6}+9 a^{6} b^{6}=a^{6} b^{6}$.

## Answer

There exist.