Repeated Manipulation

Algebra Level 3

If \(\frac{b}{b^2+1}=\frac{1}{5}\) and \(\frac{b^3}{b^6+b^5+b^4+b^3+b^2+b+1}=\frac{m}{n}\) such that \(m\) and \(n\) are positive coprime integers, find \(m+n\).

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