2000 AIME I Problem 7

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.