Given that \( ABCD\) is a square of side length \(6\). \(E\) is a point on the circumference of the circle with \(AB\) as diameter such that \(\angle CBE\) equals to \({ 30 }^{ \circ }\). The areas of \(\Delta ACE\) and \(\Delta ABE\) are \(a\) and \(b\) respectively. Find \(\left\lfloor a+b \right\rfloor \) where \(\left\lfloor x \right\rfloor \) represents the greatest integer lesser than or equal to \(x\).

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