Let $\ell$ be a real number satisfying the equation $\frac{(1+\ell)^2}{1+\ell^2}=\frac{13}{37}$. Then
\[\frac{(1+\ell)^3}{1+\ell^3}=\frac{m}{n},\] where $m$ and $n$ are positive coprime integers. Find $m+n$.

Let's think step by step and output the final answer within \boxed{}.
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