At the office we have 2 x55's and a x53. All use the same ribbon connection system so in this case I think you need to jury rig it with tape and maybe a bit of FOAM that will apply pressure to the area to hold it in place.
The connector would have to be scavenged off a board from say ebay so for me I think I'd get creative and find a way with some foam and tape.
Our x53 was bought in 2012 so it's at the end of its life. I would not fix it if badly broken.
I have an old Asus X53u laptop that I’m trying to reuse for school purposes. I was cleaning the inside of the device when the keyboard connector on the motherboard broke. The plastic piece that lifts up and down to secure the ribbon cable broke off. One of the tips is missing. The keyboard still works when perfectly lined up and taped but wares loose eventually. I’m looking for a Plastic connector piece to replace mine. Anyone know where to get it?

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