This doesn't break people out of national level thinking by itself. There are millions of people that know the basic LTV but are still solely focused on workers within their own borders, consuming news only about what's within their own borders, etc etc. These people become marxist sympathisers certainly but they're still national. They have no international solidarity in part because they have no international education. They don't know what other proletarian movements are doing and many do not care. They only care about their own conditions, or in some cases certain movements have managed to gain national success (free palestine) these are fringe cases though.