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Algebra Level 3

\[ \begin{cases} (x+y+z)(x+y)=30\\ (x+y+z)(y+z)=18\\ (x+y+z)(z+x)=2 \end{cases} \]

Given that \(x, y\) and \( z\) satisfy the system of equations above, find the sum of all values of \(z\).

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