Exponential + Logarithm Equation

Algebra Level 4

\[\Large 3^x\cdot8^{\frac{x}{x+2}}=6\]

If the sum of all real solutions can be represented by \(-a-b\log_cd\) when \(a,b,c\) and \(d\) are positive integers and \(b>1\). Find the minimum value of \(a+b+c+d\).

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