# "Surprise!" said c

$\displaystyle \large a!b! = a! + b! + c^2$

Positive integers $$a$$, $$b$$, and $$c$$, with $$a > b$$, are the unique solution to the equation above.

If $$\dfrac {a^b}{c} = \dfrac mn$$ for coprime positive integers $$m$$ and $$n$$, find $$m + n$$.

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