A Cubic with Symmetric Clues

Let $P(x)$ be a polynomial of degree 3 satisfying $P(2)=6, P(6)=2$, and $P(1)=P(8)$. There exist positive integers $a$ different from 2 and 6, and $b$ such that $P(a)=b$, for any $P$ satisfying these conditions. What is $a+b$?