mapping M-right/left to switch tabs

I would like to use M-right/left to move between tabs
- without leaving the mode I have set in the tab.

:map <M-Right> :tabnext<CR>

works in normal mode. For insert mode I could use

:imap <M-Right> <ESC>:tabnext<CR>

but then when I'll come back to the tab I was,
I have to set insert mode again.

Is there a way to keep mode in the tab?

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