This website contains a much cleaner solution, it leaves pip intact as-well and one can easily switch between 3.5 and 3.6 and then whenever 3.7 is released.
http://ubuntuhandbook.org/index.php/2017/07/install-python-3-6-1-in-ubuntu-16-04-lts/
A short summary:
sudo apt-get install python python-pip python3 python3-pip
sudo add-apt-repository ppa:jonathonf/python-3.6
sudo apt-get update
sudo apt-get install python3.6
sudo update-alternatives --install /usr/bin/python3 python3 /usr/bin/python3.5 1
sudo update-alternatives --install /usr/bin/python3 python3 /usr/bin/python3.6 2
Then
$ pip -V
pip 8.1.1 from /usr/lib/python2.7/dist-packages (python 2.7)
$ pip3 -V
pip 8.1.1 from /usr/local/lib/python3.5/dist-packages (python 3.5)
Then to select python 3.6 run
sudo update-alternatives --config python3
and select '2'. Then
$ pip3 -V
pip 8.1.1 from /usr/local/lib/python3.6/dist-packages (python 3.6)
To update pip select the desired version and
pip3 install --upgrade pip
$ pip3 -V
pip 9.0.1 from /usr/local/lib/python3.6/dist-packages (python 3.6)
Tested on Ubuntu 16.04.