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Let $f(x)$ and $g(x)$ be monic cubic polynomials, such that

$f(x)+g(x) = p (x)$,

$p(1) = 13$,

$p(3) = 97$,

$p(5) = 349$,

$f(7) = 491$,

$g(19) = 6938$, and

$g(x)$ is a depressed cubic polynomial.

Evaluate $f(30) + g (27)$.

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