Difference of cubic vieta's

Algebra Level 3

Let \(a,b,\) and \(c\) be the roots of the equation \(2x^{3}-x^{2}+x+3=0\). Find the value of the expression below.

\[ \large \frac{a^{3}-b^{3}}{a-b}+\frac{b^{3}-c^{3}}{b-c}+\frac{c^{3}-a^{3}}{c-a}\]