Achieving the global benefits of artificial intelligence (AI) will require international cooperation on many areas of governance and ethical standards, while allowing for diverse cultural perspectives and priorities. There are many barriers to achieving this at present, including mistrust between cultures, and more practical challenges of coordinating across different locations. This paper focuses particularly on barriers to cooperation between Europe and North America on the one hand and East Asia on the other, as regions which currently have an outsized impact on the development of AI ethics and governance. We suggest that there is reason to be optimistic about achieving greater cross-cultural cooperation on AI ethics and governance. We argue that misunderstandings between cultures and regions play a more important role in undermining cross-cultural trust, relative to fundamental disagreements, than is often supposed. Even where fundamental differences exist, these may not necessarily prevent productive cross-cultural cooperation, for two reasons: (1) cooperation does not require achieving agreement on principles and standards for all areas of AI; and (2) it is sometimes possible to reach agreement on practical issues despite disagreement on more abstract values or principles. We believe that academia has a key role to play in promoting cross-cultural cooperation on AI ethics and governance, by building greater mutual understanding, and clarifying where different forms of agreement will be both necessary and possible. We make a number of recommendations for practical steps and initiatives, including translation and multilingual publication of key documents, researcher exchange programmes, and development of research agendas on cross-cultural topics.