2021 AIME I Problem 1

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.

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.