An algebra problem by Abhay Kumar

Algebra Level 4

If \(\alpha\), \(\beta\) and \(\gamma\) are roots of equation \(x^3+4x+1\).Then, find \(\left(\dfrac{1}{\alpha+\beta}+\dfrac{\alpha+\beta}{\gamma^2}\right)+\left(\dfrac{1}{\beta+\gamma}+\dfrac{\beta+\gamma}{\alpha^2}\right)+\left(\dfrac{1}{\gamma+\alpha}+\dfrac{\gamma+\alpha}{\beta^2}\right)\)