Logs are cool

Algebra Level 3

Solve
\[\large \log_{2x+3}(6x^{2}+23x+21) = 4-\log_{3x+7} (4x^{2}+12x+9)\]

Let the only solution. of \(x\) in the above equation be represented as \(-\dfrac{m}{n}\), where \(m\) and \(n\) are coprime positive integers. Find \(m+n\).

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