Can I play minecraft xbox 360 edition on the xbox one

Minecraft: Xbox 360 Edition can only be played with other Xbox 360 consoles on Xbox Live. The Xbox One edition can only be played online with other Xbox One consoles. There is no cross-platform play between the Xbox editions and other editions of Minecraft.

For more info: https://support.xbox.com/en-US/games/game-titles/minecraft-version-differences

Minecraft: Xbox 360 Edition can only be played with other Xbox 360 consoles
onXbox Live. The Xbox One edition can only be played online with other Xbox Oneconsoles.
There is no cross-platform play between the Xbox editions and other editions of Minecraft.

https://support.xbox.com/games/game-titles/minecraft-version-differences

Playing Minecraft between devices and platforms

You can play Minecraft: Windows 10 Edition with other devices running Minecraft: Pocket Edition, such as Windows 10 and Windows Phone devices.
If you have Minecraft: Apple TV Edition, you can play locally with other players running a version of Minecraft: Pocket Edition. Visit Minecraft: Apple TV Edition overview
for more info.

Minecraft: Xbox 360 Edition can only be played with other Xbox 360 consoles on Xbox Live. The Xbox One edition can only be played online with other Xbox One consoles. There is no cross-platform play between the Xbox editions and other editions of Minecraft.

In this case you can transfer worlds worlds from Minecraft Xbox 360 Edition to Minecraft Xbox One Edition or/and Minecraft Xbox One Edition to Minecraft.

Cheers!

Back then when the Xbox One Edition (the Minecraft with the "Xbox One Edition" in the name, not the new "Minecraft" for Xbox One) was released, there was a short time, where you could buy "Minecraft Xbox One Edition" for a reduced price, if you owned the
original Xbox 360 Minecraft digitally.

Xbox 360 Minecraft and Xbox One Edition Minecraft are two different things. Like having a vinyl record of a music album and then having to buy a CD of the same album. Or having a DVD of a movie, and having to pay for the BluRay version of the movie.

However, the Xbox One Edition can't be bought nowadays anymore. Have you had the Xbox One Edition digitally, you would get the "Minecraft" (without the "Xbox One Edition" in the name) for free.

You can however transfer your Xbox 360 worlds to the Xbox One, if you somehow got hold of the "Xbox One Edition" before it was replaced by the new "Minecraft".

To do that, start your Xbox 360 Minecraft and make sure it's on the latest version. Then use the menu entry to upload your world to the online cloud.

Now start up Minecraft Xbox One Edition and import your world.

With your world in the Xbox One Edition, you can then start the "new" Minecraft on the Xbox One, and import your world from the Xbox One Edition to the new Minecraft.