Simple Integers

$\frac{n^3-432n+2018}{n+12}=k$

For $n\in\mathbb N$ find the number of values of $n$ such that the $k$ as defined above is an integer and also find the largest possible value of $n$ for which $k$ is an integer.

If the the number of values of $n$ is $a$ and the largest possible value of $n$ is $b$ , then enter your answer as $a+b$ .

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