Zack keeps cutting the interval $[0, 1]$ of the number line, each time cutting at a uniformly random point in the interval, until the interval is cut into pieces, none of which have length greater than $\frac35$ . The expected number of cuts that Zack makes can be written as $\frac{p}{q}$ for $p$ and $q$ relatively prime positive integers. Find $p + q$.

Let's think step by step and output the final answer within \boxed{}.
user