Let r_{1}, r_{2}, \ldots, r_{20} be the roots of the polynomial x^{20}-7 x^{3}+1. If
\frac{1}{r_{1}^{2}+1}+\frac{1}{r_{2}^{2}+1}+\cdots+\frac{1}{r_{20}^{2}+1}
can be written in the form \frac{m}{n} where m and n are positive coprime integers, find m+n.