Brain hammering question!

Calculus Level 5

If the equation \({ x }^{ 6 }-{ 54x }^{ 5 }+{ 1215x }^{ 4 }+{ 20cx }^{ 3 }+{ 15dx }^{ 2 }+{ 6ex }+{ f }=0\) has \(6\) real roots, find the value of \(c+d+e+f\).

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