If $a, b, c>0$ and $a+b+c=1$,
the minimum value of
$(a+\frac{1}{a})^{10}+(b+\frac{1}{b})^{10}+(c+\frac{1}{c})^{10}$ can be expressed as
$\frac{10^{d}}{3^{e}}$ where $d$ and $e$ are positive integers.
Find $d+e$

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