Maybe it's time to start working with DateTime? It's pretty complex in modyfing dates. For example, creating date time from your $start would look like this:
$start="2014-04-29 11:00:00";
$dateTime=DateTime::createFromFormat("Y-m-d H:m:i", $start);
And as you have $dateTime, you can modify it by one day:
$dateTime->modify('+1 day');
//or just
$dateTime->modify('next tuesday');
//and return it as string
echo $dateTime->format("M d, Y H:m:i");
DateTime understands everything that strtotime does, so it can improve your solution. Try it out yourself, and let me know if this helps.