How to round up millis() when divided into minutes?
To round to the nearest X in fixed point arithmetic: add 1/2 X (in the base units, msec, in this case) and divide by X (again, in the base units) so:
milliseconds = (milliseconds + (30*1000L))/(60*1000L);

The addition of 1/2 X causes a carry of one whole X if the fractional X in the original quantity was 1/2 X or greater. (Likewise, if the fractional X was less than 1/2 X, no carry will result).

Integer division naturally truncates any fractional amounts, so you'll be left with the rounded integer result.