For what real value of $m$ such that $\displaystyle\sum_{n=1}^\infty \frac{n^m}{m^n} $ is minimized?

I've been told that it's equivalent of solving for $ \text{Li}_{-n}\left(\frac1n\right)$ for the polylogarithmic function.

Is there a way to solve this other than by plug and chug?

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    – AlexR
    Jun 13 '15 at 16:50
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    Jun 13 '15 at 16:51

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