Let $X = \{x \in \mathbb{N} : 1 \leq x \leq 17\}$ and $Y = \{ax + b : x \in X,\; a \in \mathbb{R},\; b \in \mathbb{R},\; a > 0\}$. If mean and variance of elements of $Y$ are $17$ and $216$ respectively, then $a + b$ is equal to :