(No links due to new-user brainfart limitations on XDA. very helpful, thank you).
This (Chinese) posting explains how to install the V6.0 ROM with root,Google play etc:
Alternatively, download this package: pan(dot)baidu(dot)com(slash)share(slash)link?share id=64032&uk=4130302605 which contains all you need (USB driver, Flash utility and the "perfect ROOT" ROM v6.0 image).
0) Back up all data on cellphone, charge it to at least 60% battery, do not connect it to the PC yet, and TURN IT OFF. Plug in USB end of the USB - micro-USB cable into the PC.
1) Unpack the RAR package
2) Rename directory to remove all Chinese characters
3) Unpack the N820_V6.0_ROOT_GMS.rar file (unpacks to N820_V6.0_ROOT_GMS).
4) Go into the 'USB驱动' directory, unzip and install the USB VCOM driver.
5) Go into the '刷机工具' directory and double-click on the Flash_tool.exe file. Click on "Scatter-loading" and point to the N820_V6.0_ROOT_GMS\MT6577_Android_scatter_emmc.txt .
6) Hit F8 or click on 'Firmware -> Upgrade'.
7) Hold down the Volume Down button and connect the phone to the PC. The button can be released when the red bar starts moving.
8) After "Firmware Upgraded" window shows, unplug phone, reboot, install and enjoy.
Pictures (and Chinese explanation) can be found here: www(dot)xiaomifood(dot)com(slash)N820V6.0ROM(slash )