Don't you love Inequalities?

Algebra Level 4

Positive real numbers \(a\), \(b\) and \(c\) are such that \(abc = 1\). Find the minimum value of \[\large \dfrac{1}{a^3(b+c)}+\dfrac{1}{b^3(c+a)}+\dfrac{1}{c^3(a+b)}\] Give your answer to the nearest tenths.


Source: an IMO problem
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