In quadrilateral \(ABCD\), \(m\angle B = m\angle C = 120^\circ\), \(AB = 3\), \(BC = 4\), and \(CD = 5\). Find the area of \(ABCD\) in the form \(\frac{k\sqrt{3}}{m}\), where \(k\) and \(m\) are integers. Please provide the value of \(k + m\).

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