A good reason to use modules is that people make many mistakes when trying to reimplement the code, like you did. You incorrectly assumed all days are 24*60*60 seconds long. Solution:

use Time::Local qw( timegm );
my ($today_y, $today_m, $today_d) = (localtime())[5,4,3];
$today_m += 1;
$today_y += 1900;

# Use gmt for date arithmetic,
# even if the date is localtime.
my $today_date = timegm(0,0,0,$today_d,$today_m-1,$today_y);

# Every day *is* 24*60*60 long in GMT.
my $plus60_date = $today_date + 24*60*60 * 60;
my ($plus60_y, $plus60_m, $plus60_d) = (gmtime($plus60_date))[5,4,3];
$plus60_m += 1;
$plus60_y += 1900;

printf("Today:      %d/%02d/%02d\n", $today_y,  $today_m,  $today_d);
printf("In 60 days: %d/%02d/%02d\n", $plus60_y, $plus60_m, $plus60_d);
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Today:      2007/08/28
In 60 days: 2007/10/27
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- ikegami