Get Client attached to a job

I'm building an integration with a third-party CRM whenever a new job is created, I want to transfer details of the job and the client to the CRM.

The problem is I can't seem to get the Client details based on a Job. The Job object, when retrieving a job, doesn't provide a Contact UUID. Listing all Jobs does return the UUID.

So, I tried using the 'Retrieve a Job Contact' with a filter on the job_uuid like so:

/api_1.0/jobcontact.json?%24filter=job_uuid=%20eq%20'e5a6b41b-ad94-48ae-a23e-1cceda5f16cb'

But I'm getting the error:

[400] Invalid Record Filter Field Specified

Can you tell me what the right approach is?