Liquid Nails is a manufacturers name. They make many different types of adhesive, caulking, sealants. Use their construction adhesive or any other construction adhesive, perfect for your application. Follow the instructions. Don't over do, just a fine bead that won't squeeze out where it will be visible. Once set up, you won't get the joint apart. It's used widely by carpenters, and cabinet installers. It will hold much better in your situation than wood glues, which have to be clamped, not just nailed or touching.