A lot will depend on circumstances and then the landlord's choice of whether to pursue another month.
Yes, your notice is 6 days short and that leaves you with a liability for the May rent (in full). However, there is a duty to mitigate which means if the landlord can re-rent the place for May 1, they will not have suffered. If you find a replacement tenant, that can solve the problem. Or you might offer to pay for an ad if it is a smaller place with no other vacancies.
Did you give a last months rent deposit? If so, let it ride for April...i.e, do not give them a rent cheque for April.
If nothing works and a new tenant is in place, and you do not pay for May, they can take legal action and recover the rent plus filing fee costs.
But maybe, you have a decent landlord who will waive the 6 days short....the superintendant is not the manager usually, so it is not up to him. Ask to speak to the manager. By the way, you can give notice any time you want to, but it is a 60 day "clear" notice...meaning you cant split months.
A tenant can move out any time they want to,,,,the issue is legal liability for rent.
One other option that does not seem to fit in your case, is just revise the notice and stay for the month of May.
Hope that helps a bit.
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