lease termination question

[Tina M mcdonald]

I have a month to month tenancy with my current tenants. Due to them breaking the terms of their lease I gave them a notice that I was to end the lease, notice was given on October 20, 2019. Georgia law requires me to give them a 60 day notice whereas they would have to only give a 30 day notice to vacate the property. My issue is I gave 60 day, they then vacated the property (without my knowledge) within 10 days. I only found out that they were gone when I texted them on November 5th that I would have to begin the eviction process for non payment of rent for November. My question is this, are they legally still bound to the lease through the 60 days or do they have to still at least give me a 30 day notice that they are leaving even though I gave them the 60 day notice already? It's a tricky situation but without warning I have no tenants in the property and I feel they owe November rent or at least through the time when I am able to get it rerented. I feel this will end up in court and want to be on the right side of the law. Thanks in advance.