Inequalities # 1

Algebra Level 4

Let $a,b,c,d$ be positive real numbers. Also $ab+bc+cd+da=1$ . Then find the minimum value of $\large\dfrac{a^3}{b+c+d} + \dfrac{b^3}{a+c+d}+ \dfrac{c^3}{a+b+d}+ \dfrac{d^3}{a+b+c}$ If your answer is of the form $\dfrac{A}{B}$ , where $A$ and $B$ are positive coprime integers. Then enter the value of $A+B$ .

Source: RMO training camp 2016