We [35f &30m] are a married couple who cannot manage conflict in a healthy way. Any tips and tricks ?

We are a happy couple , married recently, after 3y being together. We are communicative , we say what bothers each other, have relationship checka monthly, play, dance etc etc. You can say, we can be a role model couple for the younger generations. However, when things are not going as planned, and one of us is angry on something , "hell" is unleashed 🙈. We fight like there's no tomorrow . I have my opinions , he has his. We can't get to a common conclusion and then we leave angry on each other...not speaking entire day. I don't know how to ..I don't even know what to ask.

I'm sure we're not the only one in this situation .. How should we start to find a way of compromise ?