Assalamualaikum brother. Indeed in your eyes cultural differences should not be a hindrance as Islam unite us as one. It is good that you talked to your parents about your intentions. However if your father still objects to your plans to marry this girl, just accept it and dua for the best as Allah Ta'ala is All Knowing and Most Merciful. Explain to the girl why both of you can't get married. For if you go against your father's wishes both of you may not live a blissful life together. Would you bear to see her suffer in marriage because of this? If you truly love her you would not want to put her in a predicament that may hurt her feelings. Inshallah everything will go smoothly and I wish both of you the best.