A little difference

Determine the value of the expression below: \[ \frac{(6! + 5!) \times (4! + 3!) \times (2! + 1!)}{(6! - 5!) \times (4! - 3!) \times (2! - 1!)}.\]

Note: The "\(!\)" symbol is the factorial operation, but there's a clever shortcut for solving this that entirely avoids multiplying out the factorials!

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