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If $x_{1},x_{2},.....,x_{71}$ satisfy

$\sum_{j=1}^{71}\frac{x_{j}}{i+j}=\frac{4}{2i+1} \text{ for } i=1,2,...,71.$

Suppose $\sum_{j=1}^{71}\frac{x_{j}}{2j+1} = \frac{p}{q},$ where $p$ and $q$ are coprime integers. Find $p+q$.

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