So Many Logs!

Algebra Level 5

\[ \large { 6 }^{ \log _{ 5 }{ x } }\log _{ 3 }( { x }^{ 5 } ) -{ 5 }^{ \log _{ 6 }{ 6x } }\log _{ 3 }{ \left( \dfrac { x }{ 3 }\right) } ={ 6 }^{ \log _{ 5 }{ 5x } }-{ 5 }^{ \log _{ 6 }{ x } }\]

If the sum of the solutions to the equation above is equal to \[\large { a }^{ \frac { b }{ c } }+d, \]

where \(a, b, c\) and \(d \) are all positive integers with \(b\) and \(c\) are coprime, what is the smallest possible value of \(abc+d\)?

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