Is there a quadrilateral $ABCD$ of area 1 such that for any point O inside it the area of at least one of the triangles $\triangle OAB, \triangle OBC, \triangle OCD,$ or $\triangle OAD$ is an irrational number? The original answer involves a trapezoid with bases m and $\sqrt[n]{p}$. Please provide the sum of m，n and p involved in the original example.

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