imc

Let $P(x)$ be the unique polynomial of minimal degree with the following properties: $P(x)$ has a leading coefficient $1$, $1$ is a root of $P(x)-1$, $2$ is a root of $P(x-2)$, $3$ is a root of $P(3x)$, and * $4$ is a root of $4P(x)$. The roots of $P(x)$ are integers, with one exception. The root that is not an integer and can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers. What is $m+n$?