Why does it always have to be maximizing?

Maximize the value of \(m+n\) where \(m\) and \(n\) are positive integers satisfying:

\[m^2+2 \cdot 3^n=m(2^{n+1}-1)\]


Inspired by an IMO problem, but pretty much nothing like it, so Daniel Liu doesn't have to worry. :D

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