Suppose that \(x,\) \(y,\) and \(z\) are three positive numbers that satisfy the equations \(xyz = 1,\) \(x + \frac {1}{z} = 5,\) and \(y + \frac {1}{x} = 29.\) Then \(z + \frac {1}{y} = \frac {m}{n},\) where \(m\) and \(n\) are relatively prime positive integers. Find \(m + n\).
(第十八届AIME1 2000 第7题)