If 1 is subtracted from the numerator and 3 is added to the denominator of a fraction, the fraction becomes \(\frac{1}{2}\). If 1 is added to the numerator and 1 is subtracted from the denominator of the original fraction, it becomes \(\frac{5}{6}\). What is the sum of the numerator and the denominator of the original fraction?

1
23
2
22
3
21
4
More than one of the above
5
None of the above

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