\[\large{\begin{cases} \sqrt x \left(1 - \dfrac{12}{3x+y} \right) = 2 \\ \sqrt y \left(1 + \dfrac{12}{3x+y} \right) = 6 \end{cases}} \]

\(x\) and \(y\) are real numbers satisfying the system of equations above.

If \(x = a + b \sqrt3\) and \(y = c + d\sqrt3\), where \(a,b,c\) and \(d\) are integers, submit your answer as \(a+b+c+d \).

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