A calculus problem by Justin Tuazon

Calculus Level pending

If the value of \( \int _{ 1 }^{ e }{ 4{ x }^{ 3 }{ \left( \ln { x } \right) }^{ 3 }dx }\) can be expressed as \(\frac { a{ e }^{ b }+c }{ d } \), where a, b, c, and d are natural numbers and a, c, and d are relatively prime, what is the value of \((a+b)-(c+d)\)?

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