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 \frac{2}{3} if they won the previous race but only \frac{1}{3} if they lost the previous race. The probability that Zou will win exactly 5 of the 6 races is \frac{m}{n}, where m and n are relatively prime positive integers. Find m+n.