Let $\gamma_i$ and $\overline{\gamma_i}$ be the 10 zeros of $x^{10}+(13x-1)^{10}$, where $i=1, 2, 3, 4, 5$. Compute $$\frac{1}{\gamma_1 \overline{\gamma_1}}+\frac{1}{\gamma_2 \overline{\gamma_2}}+\cdots+\frac{1}{\gamma_5 \overline{\gamma_5}}$$