Writer's Fallout Shelter

To be successful, when writing we need to make our work have the broadest appeal possible, a universality that speaks to people other than ourselves. At the same time, we need to write about things that matter to us and things that we know so the writing rings true.

How do you balance the two out? How can you take what matters to you and the things that are incredibly personal and give them universal appeal? Do we just have to depend on luck, that our audience has had similar experiences and will recognize themselves in the situations we describe or is there something we need to do deliberately to make this happen?