It's not important to know the provider when dialing Bolivia from abroad. To be honest I am not aware of cell phones starting with digit 6. My sources tell me that cell phones start with 7. It is possible however for the Bolivian telecom authorities to have in the meantime introduced a new dialing format with 6 being the starting digit. If your cell number is correct and you have also tried using 011 instead of the plus sign in the beginning (011 591 6??? ????) with no success, then there is likely an issue on your end. For instance, your phone service may not allow dialing international calls.
I can help you by trying to dial this number for you. If it works then the problem is on your end. If you want to do this go ahead and send me the number using the Contact button at the top right of this page.