Is cubic a prime?

Number Theory Level 5

$\Large x^3-44x^2+556x-1805$

Let $x_1,x_2,x_3,\dots x_n$ be the positive integers that make the above expression a (positive) prime number. Then, find the value of $\displaystyle \sum_{i=1}^n x_i$ .

Is cubic a prime?

Also try Is Quartic a square?