Let a >0. If the function f(x)=6 x^3-45 a x^2+108 a^2 x+1 attains its local maximum and minimum values at the points x_1 and x_2 respectively such…

Let $\displaystyle \mathrm{a}>0$. If the function $\displaystyle f(x)=6 x^3-45 \mathrm{a} x^2+108 \mathrm{a}^2 x+1$ attains its local maximum and minimum values at the points $\displaystyle x_1$ and $\displaystyle x_2$ respectively such that $\displaystyle x_1 x_2=54$, then a $\displaystyle +x_1+x_2$ is equal to :