In square \(ABCE\), \(AF=2FE\) and \(CD=2DE\). What is the ratio of the area of \(\triangle BFD\) to the area of square \(ABCE\)? The answer is in the form \(\frac{k}{m}\), please find the value of \(k + m\).

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