A cyclic inequality with 4 variables

Algebra Level 5

\[\large x^4y^2+y^4z^2+z^4t^2+t^4x^2+2016x^4y^4z^4t^4\]

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 \(a+b\).

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