Make sure to take care of the carry. As to a simple solution, you don't even need a scanner:
NSString *timeStr = @"23:59";
NSArray *comps = [timeStr componentsSeparatedByString:@":"];
int h = [comps[0] intValue];
int m = [comps[1] intValue];
h += (m + 1) / 60;
h %= 24;
m = (m + 1) % 60;
NSLog(@"The new time is: %02d:%02d", h, m);