No need of any jugglery - 2

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 $x$ .