A clean way without having to uninstall a previous version or reverting to additional software like Anaconda or docker, etc. is to download the Python 3.6 source code and install it as follows:
$ mkdir /home/<user>/python3.6
$ ./configure --prefix=/home/<user>/python3.6/
$ make altinstall
To use it you either:
add /home/<user>/python3.6/bin to your PATH (and lib to LD_LIBRARY_PATH) and be done with it. (You may also need to add to your include path etc., depending on what you're trying to achieve exactly - but you get the idea, I hope.);
or, you create a virtual environment similar to this: /home/<user>/python3.6/bin/python3.6 -m venv env-python3.6.
No sudo or root access required. No messing up your system.