Extraordinary Polynomial

$ax^3+bx^{2}+cx+d$ is a cubic polynomial,

where $(a,b,c,d)\epsilon N$

has real roots $x_{1},x_{2},x_{3}$

such that ,

$f(2)=140$

$f(3)=240$

$f(5)=560$

$f(7)=1080$

Then evaluate ,

$(\sum_{i=1}^{3}2+x_{i}) + (\sum_{i=1}^{3}3+x_{i})+(\sum_{i=1}^{3}5+x_{i})$