Consider all polynomials $f(x)$ of degree 6 such that $f(n)$ is an integer for all integers $n$. The smallest possible positive leading coefficient of $f(n)$ can be expressed as $\frac{a}{b}$, where $a$ and $b$ are positive coprime integers. What is the value of $a+b$?

Your answer seems reasonable.
Find out if you're right!