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Algebra Level 5

Consider the following equation in '\( x \)' : \[ \log_{2x+3} (6x^2 + 23x + 21) = 4 - \log_{3x+7} (4x^2 + 12x + 9) \]

The sum of possible values of '\( x \)' satisfying the above equation is of the form \( \dfrac{-a}{b} \) ; where \( a \) and \( b \) are co-prime integers.

Find \( \mathbb{ a + b } \)

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