$\Delta ABC$, $AB=17$, $BC=25$, and $AC=26$. Square $JKLM$ is such that $\overline{JK}$ lies on $\overline{AB}$, $L$ lies on $\overline{BC}$, and $M$ lies on $\overline{AC}$. The length of one side of $JKLM$ can be written as $\frac{m}{n}$, where $m$ and $n$ are positive, coprime integers. Find $m+n$.

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