Orthocenter and Parallelogram

Geometry Level 5

In triangle \(ABC\) with \(AB=13, BC=14, CA=15\) and orthocenter \(H,\) let \(N\) be the midpoint of \(AH\) and let \(M\) be a point such that \(BHCM\) is a parallelogram. If \(MN\) intersects \(BC\) at \(P\), then \(\dfrac{BP}{PC}=\dfrac{m}{n}\) for some relatively prime positive integers \(m\) and \(n\). Find \(m+n\).

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