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Algebra Level 4

\[\large { 2 }^{ a }+{ 2 }^{ b }+{ 2 }^{ c }+{ 2 }^{ 13 }={ 2 }^{ d }\]

Given that \(a,b,c,d\) are positive integers that satisfy the above equation.Then what is the maximum value of \(a+b+c+d\) ?

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