# Is This Enough Information?

Geometry Level 4

A right triangle has legs $a$ and $b$, and hypotenuse $c$.

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

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

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