Making a JMX connection from a client deployed in EAP 6 to an EAP 5 server

Issue

We need to connect from a servlet deployed in JBoss EAP 6.0.1 via JMX to a JBoss EAP 5 server.
This fails with:

Caused by: java.io.IOException: Failed to retrieve RMIServer stub: javax.naming.NameNotFoundException: rmi://127.0.0.1:9999/jmxrmi -- service jboss.naming.context.java.rmi:."127.0.0.1:9999".jmxrmi
    at javax.management.remote.rmi.RMIConnector.connect(RMIConnector.java:340) [:1.6.0_26]
    at javax.management.remote.JMXConnectorFactory.connect(JMXConnectorFactory.java:248) [:1.6.0_26]
    at com.example.JMXConnectionBean.init(JMXConnectionBean.java:28)
[snip]
Caused by: javax.naming.NameNotFoundException: rmi://127.0.0.1:9999/jmxrmi -- service jboss.naming.context.java.rmi:."127.0.0.1:9999".jmxrmi
    at org.jboss.as.naming.ServiceBasedNamingStore.lookup(ServiceBasedNamingStore.java:87)
    at org.jboss.as.naming.NamingContext.lookup(NamingContext.java:173)
    at org.jboss.as.naming.InitialContext.lookup(InitialContext.java:47)
    at org.jboss.as.naming.NamingContext.lookup(NamingContext.java:209)
    at javax.naming.InitialContext.lookup(InitialContext.java:392) [:1.6.0_26]
    at javax.management.remote.rmi.RMIConnector.findRMIServerJNDI(RMIConnector.java:1888) [:1.6.0_26]
    at javax.management.remote.rmi.RMIConnector.findRMIServer(RMIConnector.java:1858) [:1.6.0_26]
    at javax.management.remote.rmi.RMIConnector.connect(RMIConnector.java:257) [:1.6.0_26]
    ... 37 more