Isn't this USAMO 2017 Problem 6

Algebra Level 3

Let \(S\) be the maximum possible value of \[\frac{a}{b^3+4}+\frac{b}{c^3+4}+\frac{c}{d^3+4}+\frac{d}{a^3+4} \]given that \(a\), \(b\), \(c\), \(d\) are nonnegative real numbers such that \(a+b+c+d=4\). Given that \(S\) can be written in the form \(\frac{m}{n}\) where \(m,n\) are coprime positive integers, find \(100m+n\).

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