Square $ABCD$ is cut by a line segment $EF$ into two rectangles $AEFD$ and $BCFE$. The lengths of the sides of each of these rectangles are positive integers. It is known that the area of the rectangle $AEFD$ is $30$ and it is larger than the area of the rectangle $BCFE$. Find the area of square $ABCD$.

Let's think step by step and output the final answer within \boxed{}.
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