# Maximum Sum of Cubic Products

Algebra Level 5

Let $x, y, z$ be non-negative real numbers satisfying the condition $x+y+z = 1$. The maximum possible value of

$x^3y^3 + y^3z^3 + z^3x^3$

has the form $\frac {a} {b} ,$ where $a$ and $b$ are positive, coprime integers. What is the value of $a+b$?

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