No Ordinary Optimization Problem

Calculus Level 3

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 $d+e$