Simplifying expression quartic x Is it possible to simplify the expression:

$3x^4-x^3+4x^2-5x-5$

by finding the different roots of x? I tried by the Rational Roots test, but couldn't find one easily.
Hint: One solution is given by $$\left\{x\to \frac{1}{12}-\frac{1}{12} \sqrt{-31-\frac{716}{\sqrt[3]{3079+6 \sqrt{422655}}}+4
   \sqrt[3]{3079+6 \sqrt{422655}}}-\frac{1}{2} \sqrt{-\frac{31}{18}+\frac{179}{9
   \sqrt[3]{3079+6 \sqrt{422655}}}-\frac{1}{9} \sqrt[3]{3079+6 \sqrt{422655}}-\frac{313}{18
   \sqrt{-31-\frac{716}{\sqrt[3]{3079+6 \sqrt{422655}}}+4 \sqrt[3]{3079+6
   \sqrt{422655}}}}}\right\}$$
Hint: One solution is given by $$\left\{x\to \frac{1}{12}-\frac{1}{12} \sqrt{-31-\frac{716}{\sqrt[3]{3079+6 \sqrt{422655}}}+4
   \sqrt[3]{3079+6 \sqrt{422655}}}-\frac{1}{2} \sqrt{-\frac{31}{18}+\frac{179}{9
   \sqrt[3]{3079+6 \sqrt{422655}}}-\frac{1}{9} \sqrt[3]{3079+6 \sqrt{422655}}-\frac{313}{18
   \sqrt{-31-\frac{716}{\sqrt[3]{3079+6 \sqrt{422655}}}+4 \sqrt[3]{3079+6
   \sqrt{422655}}}}}\right\}$$