riddle - square number year, cube number day, when was I born?

At the year of a square number,
My age will be it's square root.
At the day of a cube number,
my month is it's cube root.
add the day and the month make them thirsty.

I'm still alive, when was I born ? (dd/mm/yyyy)

Answer

My attempt:

27/03/1980, 2025 is 45 squared, 27 is a cube, and 27+3=30 (thirsty)