Calculating millisecond and avoiding float numbers

I have a variable which increases/decreases from 0 to 255 every (X) millisecond. so:

(X) x 255 = time in millisecond / 60000 = minute 

(X) millisecond is a variable which increases only by it self, for example after each button press:

(X) + (X) x 255 = time in millisecond / 60000 = minute (X) + (X) + (X) x 255 = time in millisecond / 60000 = minute etc 

What number should we use in (X) so every time it increases i get +1 minute in output. I want an integer number not a float.

The language is C++ if it helps in anyway…