A cyclic inequality with 4 variables

$\large x^4y^2+y^4z^2+z^4t^2+t^4x^2+2016x^4y^4z^4t^4$

Let $M$ be the maximum value of the above expression for non-negative reals $x,y,z,t$ given $x+y+z+t=1$ .

Given that $M$ can be expressed as $\dfrac{a}{b}$ where $a, b$ are positive integers and $\gcd(a,b)=1$ .

Find $a+b$ .