\[ \begin{cases} x + xy + xyz = 12 \\ y + yz + xyz = 21 \\ z + zx + xyz = 30 \end{cases} \]

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

Give your answer to 3 decimal places.

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