Zou and Chou are practicing their \(100\)-meter sprints by running \(6\) races against each other. Zou wins the first race, and after that, the probability that one of them wins a race is \(\frac23\) if they won the previous race but only \(\frac13\) if they lost the previous race. The probability that Zou will win exactly \(5\) of the \(6\) races is \(\frac mn\), where \(m\) and \(n\) are relatively prime positive integers. Find \(m+n.\)