Wrong. You're a different country despite sharing language and culture with the mainland. How many people recognize you compare to your comrades? Did forming a separate government off an island make you an identity? It didn't despite the language factor.
BTW there is a common language in India which is Hindi. Unlike your communist counterpart, here it is not mandated but left to the people to learn it. Even in the deepest parts of southern and eastern India, people today know Hindi thanks to the spread of bollywood and entertainment industry.
Let me give you an example; my mother language is Denzongkha which I speak with my parents and siblings. However, when I am with my friends from other states, I speak in Hindi which even they do and I am talking about friends from southern India, western India and of course my adjoining regions.
We have our bits and pieces of regional accents but we understand each other very well.
Here, common language is taught through arts, culture, music etc rather than at a political party's gunpoint (hint hint: Mandarin).
Out nation's linguistic structure baffles many countries but that is only because they don't understand Indian cultural mindset.