Setting up the ability to ssh into a layer 2 switch

Hello Cisco Experts,

This is going to seem like a basic question, but I’m going to ask it any ways.  Let’s say I have the following setup:
•      A layer 3 (Cisco 3560) distribution layer switch.  This switch is named DIST-SW1.
•      DIST-SW1 has two vlans (vlan 10 and vlan 20).
•      The network associated with vlan 10 is 10.110.10.0 /24
•      The network associated with vlan20 is 10.110.20.0 /24
•      Loopback0 on DIST-SW1 has the IP of 10.10.10.12 255.255.255.0
•      A layer 2 (Cisco 2960) access layer switch.  This switch in named ACCS-SW1
•      ACCS-SW1 is connected to DIST-SW1 via a trunk
•      All of the ports on ACCS-SW1 are on vlan10
•      Loopback0 on ACCS-SW1 has the IP address of 10.10.10.15 255.255.255.0

If I want to ssh into DIST-SW1, I do so using the ip of 10.10.10.12.  I want to be able to SSH into ACCS-SW1 as well.  When I try to ssh to 10.10.10.15, there is no connection.  When I try to ping 10.10.10.15, I get no reply.  If I look at the routing table in DIST-SW1, I don’t see a route to get me to 10.10.10.15.  This explains why the ping doesn’t work.  My thought to be able to ssh into ACCS-SW1 is to change the ip of loopback0 to an IP on the 10.110.10.0 network.  Unfortunately I don’t have a lab to test this on right now, so I’m asking.  Is this the right approach?

Thanks,
Nick