\[\large\sum_{\text{cyc}\{a,b,c\}}\left( \dfrac{a}{b}\right) + \dfrac{3k\sqrt[3]{abc}}{\displaystyle\sum_{\text{cyc}} a} \geq 5\]

If \(a,b\) and \(c\) are positive numbers such that equation above is true, find the value of \(k\).

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