There's a book, "Nonviolent communication: a language of life", 3rd ed, which writes about this.
From what I remember, if you can talk and listen to the kid, and understand what underlying needs drive the behavior, and then mention this to him -- then he'll feel understood, and notice that you're listening and care. And that was, from what I remember, the most important thing, in solving a conflict. (I.e. being listened to and understood.) The other things then, afterwards, tended to be comparatively simple to solve together.
Yes. Telling the child your own needs and feelings is not enough, you need to ask about and listen intently for the needs and feeling of your child. Only when both you and your child both feel heard and seen will understanding result. And once you have understanding of each other then you both know what to do to take best care of each other. The solutions to the conflict then come by themselves, because you now understand each others needs. This only happens after you've put in the hard work to listen and talk and listen and talk and listen and talk and listen some more...
From what I remember, if you can talk and listen to the kid, and understand what underlying needs drive the behavior, and then mention this to him -- then he'll feel understood, and notice that you're listening and care. And that was, from what I remember, the most important thing, in solving a conflict. (I.e. being listened to and understood.) The other things then, afterwards, tended to be comparatively simple to solve together.