The equation
x^{10}+(13 x-1)^{10}=0
has 10 complex roots r_{1}, \overline{R_{1}}, r_{2}, \overline{R_{2}}, r_{3}, \overline{R_{3}}, r_{4}, \overline{R_{4}}, r_{5}, \overline{R_{5}}, where the bar denotes complex conjugation. Find the value of
\frac{1}{r_{1} \overline{R_{1}}}+\frac{1}{r_{2} \overline{R_{2}}}+\frac{1}{r_{3} \overline{R_{3}}}+\frac{1}{r_{4} \overline{R_{4}}}+\frac{1}{r_{5} \overline{R_{5}}}