Let $p(x) = x^2 - 5x + a$ and $q(x) = x^2 - 3x + b$, where $a$ and $b$ are positive integers. Suppose $\text{hcf}(p(x), q(x)) = x - 1$ and $k(x) = \text{lcm}(p(x), q(x))$. If the coefficient of the highest degree term of $k(x)$ is $1$, the sum of the roots of $(x-1) + k(x)$ is