BMO maximum

Algebra Level 4

If the maximum value of the expression $$x^2y-y^2x$$ with $$0\leq x\leq1$$ and $$0\leq y\leq1$$ can be expressed as $$\frac{m}{n}$$ with $$m$$ and $$n$$ co-prime integer numbers find the value $$m+n$$

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