How should I go about sealing/blocking this gap/hole?

I recently moved into a new apartment a week ago and there is a minor roach issue. I’m working on sealing/blocking the gaps/holes like such to completely seal off my home and eliminate any opening possible before it gets worse. It’s the only way to permanently fix any insect issue. I couldn’t care less about the... show more I recently moved into a new apartment a week ago and there is a minor roach issue. I’m working on sealing/blocking the gaps/holes like such to completely seal off my home and eliminate any opening possible before it gets worse. It’s the only way to permanently fix any insect issue.

I couldn’t care less about the look of the sealing/blockage. I just want a fast, easy, and permanent way to have this gap closed off. I plan to Flex Glue the other cracks/minor openings in the corners (would that work for this as well? I assumed not as the opening seemed too large but wasn’t positive) . This gap here consist of my dishwasher, drywall, and wooden cabinet at the top and is about 6 inches tall 4 inches wide. Thanks for the help.
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