# Maxima and Minima

Calculus Level 5

Subject to $$x+y=1$$ for positive reals, the maximum and local minimum of $x^4 y + y^4 x$ can be expressed as $$\frac{a}{b}$$ and $$\frac{c}{d}$$, respectively, where $$a,b$$ and $$c,d$$ are pairs of positive coprime integers.

Find $$a+b+c+d$$.

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