Teve o mesmo problema no Ubuntu 15.04
Resolva-o criando um novo arquivo: /etc/systemd/system/plexmediaserver.service
Posteriormente, cole o seguinte:
[Unit]
Description=Plex Media Server for Linux
After=network.target
[Service]
Environment="PLEX_MEDIA_SERVER_APPLICATION_SUPPORT_DIR=/var/lib/plexmediaserver/Library/Application Support"
Environment=PLEX_MEDIA_SERVER_HOME=/usr/lib/plexmediaserver
Environment=PLEX_MEDIA_SERVER_MAX_PLUGIN_PROCS=6
Environment=PLEX_MEDIA_SERVER_TMPDIR=/tmp
Environment=LD_LIBRARY_PATH=/usr/lib/plexmediaserver
Environment=LC_ALL=en_US.UTF-8
Environment=LANG=en_US.UTF-8
ExecStartPre=/bin/sh -c '/usr/bin/test -d "${PLEX_MEDIA_SERVER_APPLICATION_SUPPORT_DIR}" || /bin/mkdir -p "${PLEX_MEDIA_SERVER_APPLICATION_SUPPORT_DIR}"'
ExecStart=/bin/sh -c '/usr/lib/plexmediaserver/Plex\ Media\ Server'
Type=simple
User=plex
Group=plex
Restart=on-failure
RestartSec=5
StartLimitInterval=60s
StartLimitBurst=3
[Install]
WantedBy=multi-user.target
Então corra, sudo service plexmediaserver start
O Plex deve iniciar normalmente e você deve acessá-lo através de: http://127.0.0.1:32400/web
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