Let $N$ be a positive multiple of $6$. One red ball and $N$ green balls are arranged in a line in random order. Let $P(N)$ be the probability that at least $\frac{5}{6}$ of the green balls are on the same side of the red ball. What is the sum of the digits of the least value of $N$ such that $P(N)<\frac{7}{20}$?