Which is correct:
Enter both the start and end date for implementation.
Enter both the start and end dates for implementation.
Why?
In your example, 'date' should remain singular.
This is because there is only one start date, and one end date. You are referring to them individually, not as a group, so neither is plural
If you said "start and end dates" it could mean there are more than one of each.
However, you could group the 'start date' and 'end date' together and say "enter the dates" if you thought there was no need to specify what the two individual dates were.
If you think about the example "men and women". These are two nouns, both plural. You understand that this must mean there are several of each. If there was only one of each, you'd say "a man and a woman". But, if you didn't need to differentiate between the man and the woman, you could group the two together and use a plural word like "people".