MySQL service doesn't create /var/run/mysqld and thus fails to start

I am running Ubuntu 15.04 which recently upgraded to MySQL 5.6. Ever since then, it's been unable to start on boot because /var/run/mysqld doesn't exist. Doing a sudo service mysql start just hangs. Creating the directory and assigning mysql:root and 755 as permissions allows mysql to start, but the folder is destroyed on every reboot.

Whenever /var/run/mysqld doesn't exist, these lines show up in /var/log/mysql/error.log:
==========================================================================
2015-03-24 17:43:15 1178 [Note] Server hostname (bind-address): '127.0.0.1'; port: 3306
2015-03-24 17:43:15 1178 [Note] - '127.0.0.1' resolves to '127.0.0.1';
2015-03-24 17:43:15 1178 [Note] Server socket created on IP: '127.0.0.1'.
2015-03-24 17:43:15 1178 [ERROR] Can't start server : Bind on unix socket: No such file or directory
2015-03-24 17:43:15 1178 [ERROR] Do you already have another mysqld server running on socket: /var/run/mysqld/mysqld.sock ?
2015-03-24 17:43:15 1178 [ERROR] Aborting

systemctl status mysql shows:
==========================================================================
Mar 24 22:43:33 benxiao-ubuntu01 systemd[1]: Starting MySQL Community Server...
Mar 24 22:43:33 benxiao-ubuntu01 mysqld_safe[1030]: 150324 22:43:33 mysqld_safe Can't log to error log and syslog at the same time. Remove all --log-error configuration options for --syslog to take effect.
Mar 24 22:43:33 benxiao-ubuntu01 mysqld_safe[1030]: 150324 22:43:33 mysqld_safe Logging to '/var/log/mysql/error.log'.
Mar 24 22:43:33 benxiao-ubuntu01 mysqld_safe[1030]: mkdir: cannot create directory ‘/var/run/mysqld’: Permission denied
Mar 24 22:43:33 benxiao-ubuntu01 mysqld_safe[1030]: chown: cannot access ‘/var/run/mysqld’: No such file or directory
Mar 24 22:43:33 benxiao-ubuntu01 mysqld_safe[1030]: chmod: cannot access ‘/var/run/mysqld’: No such file or directory
Mar 24 22:43:33 benxiao-ubuntu01 mysqld_safe[1030]: 150324 22:43:33 mysqld_safe Starting mysqld daemon with databases from /var/lib/mysql

ProblemType: Bug
DistroRelease: Ubuntu 15.04
Package: mysql-server-5.6 5.6.23-1~exp1~ubuntu4
ProcVersionSignature: Ubuntu 3.19.0-10.10-generic 3.19.2
Uname: Linux 3.19.0-10-generic x86_64
ApportVersion: 2.16.2-0ubuntu4
Architecture: amd64
Date: Tue Mar 24 17:47:58 2015
InstallationDate: Installed on 2015-02-15 (37 days ago)
InstallationMedia: Ubuntu 15.04 "Vivid Vervet" - Alpha amd64 (20150119)
ProcEnviron:
 TERM=xterm
 PATH=(custom, no user)
 XDG_RUNTIME_DIR=<set>
 LANG=en_US.UTF-8
 SHELL=/bin/bash
SourcePackage: mysql-5.6
UpgradeStatus: No upgrade log present (probably fresh install)