Calvin goes to the local "7-11" store!

Calvin goes into the local "7-11" store and buys four items. The bill totals \($7.11\) . He notices that the product of the four prices is also exactly \(7.11\) .

If the ascending order of the prices of the four items in dollars is \(A, B, C, D\) , and then, if the value of \(\dfrac{D}{B} + \dfrac{C}{A} \) can be expressed as \(\dfrac{M}{N}\) for positive coprime integers \((M,N)\). Submit the value of \(M+N\) as your answer.

Note : The four numbers \((A,B,C,D)\) have at most two places of decimals.

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