Integers...

Algebra Level 3

If \(x,y,z\) are three consecutive positive integers such that \(\frac { x }{ y } +\frac { y }{ z } +\frac { z }{ x } +\frac { y }{ x } +\frac { x }{ z } +\frac { z }{ y } \) is an integer, What is the value of \(x+y+z\) ?

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