Let's fight inequality

Algebra Level 3

\[\begin{cases} \dfrac{6x^{2}}{1+9x^{2}}=y \\ \dfrac{6y^{2}}{1+9y^{2}}=z \\ \dfrac{6z^{2}}{1+9z^{2}}=x \end{cases} \]

Find the sum of \(x+y+z\) of all the ordered real triplets \((x, y, z)\) satisfying the system of equations above.

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