Is it possible to apply for X1 visa in another country?

Hello there. I am an Eritrean, a country located in East Africa. I wanted to go to Ethiopia, another country in East Africa, and then ask for X1 to go to China. I have passport, admission letter of the university which accepted me for scholarship. Is it possible for me to get my entry visa from Ethiopia while I am an Eritrean. Thanks for your quick responses.