Seems like Cauchy

Algebra Level 4

The maximum value of $$f(x,y,z) = 5x+4y+4z$$ on the ellipsoid $$10x^2 + 20y^2 + 15z^2 = 1$$ can be expressed in the form $$\sqrt{ \dfrac{m}{n}}$$, where $$m$$ and $$n$$ are coprime positive integers. Find $$m+n$$.

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