If \(x\), \(y\) and \(z\) are real numbers such that the three vectors \[\overrightarrow{a} = (x, 2, -4), \overrightarrow{b} = (1, y, 3), \overrightarrow{c} = (1, -2, z)\] are pairwise perpendicular to each other, what is \(x+y+z\)?

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