# 1.333333333333

Algebra Level 4

If $$x+y+z=2196$$

$$\sqrt [ 3 ]{ x } +y+z=2076$$

$$x+\sqrt [ 3 ]{ y } +z=1860$$

$$x+y+\sqrt [ 3 ]{ z } =480$$

and if $$x$$, $$y$$ and $$z$$ are positive integers,

Find $${ x }^{ \frac { 2 }{ 3 } }+{ y }^{ \frac { 2 }{ 3 } }+{ z }^{ \frac { 2 }{ 3 } }$$

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