An inequality problem by Gurido Cuong

Algebra Level 5

\[ \dfrac{1}{\sqrt[3]{a+3b}}+\dfrac{1}{\sqrt[3]{b+3c}}+\dfrac{1}{\sqrt[3]{c+3a-d}}-24abc+12abcd\] If \(a,b\) and \(c\) are positive reals satisfying \(a+b+c=\dfrac{3}{4}\) and \(d\) is a non-negative real, minimize the expression above to 3 decimal places

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