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Geometry Level 4

A right triangle has legs aa and bb, and hypotenuse cc.

The length of the median to the hypotenuse is a3b+b3a3\sqrt[3]{a^{3}b+b^{3}a}.

If the length of the altitude to the hypotenuse can be expressed in the form mn\dfrac{m}{n} for coprime positive integers mm and nn, find m+nm+n.

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