# 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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