Rumi was a Bactrian poet (some claim Persian, Iranian, Afghan, and Turkish as empires have come and gone), who lived 800 years ago and traveled widely. Bactria was next to the Buddhist center of Gandhara, part of the Indian empire. (See map below). Rumi represents a school of Islamic mysticism known as Sufism.
This tradition shares elements and qualities that make it more like Hinduism, Buddhism, and shamanism than orthodox, very non-mystical Islam. Its essential message is the oneness of human beings and the divine world[s]. This merging (in Buddhism, non-dualism; in Hinduism, yoga or union) of the individual with the whole is a classic characteristic of mysticism. While many claim Rumi as their own, he in fact belongs to our collective world heritage.
Bactria: Greco-Bactrian Empire (Wiki)