Logical Riddle

The 'Math Department Lunch' is in March, but I forgot which day, so I asked around.
Denise said that the date was an odd number; Kristell claimed it was greater than 13. Wanda declared it was not a perfect square, while Linda swore it was a perfect cube. Finally, Anthony told me the date was less than one-fourth his age, which I know to be 68.
Yesterday I learned that only one of them had told the truth!
What is the date of the lunch?