Three Equations, Three Variables!

Algebra Level 4

\[\large{\begin{cases}{x^3 + x(y-z)^2 = 2} \\ {y^3 + y(z-x)^2 = 30} \\{z^3 + z(x-y)^2 = 16} \end{cases}}\]

Find the sum of all real \(x,y,z\) for which the above system of equations satisfies.

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