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Algebra Level 4

\[ \large { \begin{eqnarray} (X+Y)(X+Y)&=&4Z-1 \\ (Y+Z)(Y+Z) &=& 4X-1 \\ (X+Z)(X+Z) & =& 4Y-1 \\ \end{eqnarray} } \]

If \(X,Y\) and \(Z\) are rational real numbers that satisfy the system of equations above, find the value of \(X+Y+Z\).

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