100 followers problem

Algebra Level 5

\[\large 4(a^6+b^6+c^6)+5abc(a^3+b^3+c^3)\]

Given that \(a\), \(b\) and \(c\) are reals satisfying \(ab+bc+ca=\sqrt[3]{100}\).

Find the minimum value of the expression above.


Source: Israel winter camp 2015 test.
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