It is given that \(\log_{6}a + \log_{6}b + \log_{6}c = 6\), where \(a\), \(b\), and \(c\) are positive integers that form an increasing geometric sequence and \(b - a\) is the square of an integer. Find \(a + b + c\).

(第二十届AIME2 2002 第3题)