Pitching a Tent

Geometry Level 5

In \(\Delta ABC\), \(AB=17\), \(BC=25\), 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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