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)