Club Truncator is in a soccer league with six other teams, each of which it plays once. In any of its 6 matches, the probabilities that Club Truncator will win, lose, or tie are each \(\frac {1}{3}\). The probability that Club Truncator will finish the season with more wins than losses is \(\frac {m}{n}\), where \(m\) and \(n\) are relatively prime positive integers. Find \(m + n\).
(第十九届AIME2 2001 第11题)