If the first half of your statement is true, then why do the billions of people subsisting on a few dollars a day around the world do not have society-wide problems with drug abuse and mental illness? Or are you implying that this causation only happens in developed countries?
What can you do to refute the idea that instead of drug abuse and mental illness being caused poverty, the same factors that predispose one to drug abuse and mental illness also predispose one to poverty?
> culture is also determined by lack of access to economic opportunities
Similarly, it's rather the other way around; lack of access to economic opportunities is caused by a culture that values human capital less. Of course, the two compound over time; but history is empirically full of examples of minority cultural groups that were discriminated against (whether legally, socially, or otherwise) but nevertheless succeeded economically due to the culture placing a high value on human capital[0].
[0]: Sowell, T. Discrimination and Disparities.