Did you encode the filter criteria like this...

%7B%22fields%22%3A%7B%22CAE%22%3A11029%7D%7D

https://ninox.com/en/manual/api/rest

I couldn't filter using a value of an array field. If someone else doesn't post a solution, you could attend one of the API webinars. Please share if you get an answer.

I doubt you'll get it working with an array (which I guess is a multi choice field or some formula returning multiple items in an array?)

I find checking for an item in an array not to be straightforward in any case in NX. My favourite approach is to concat the array and figure out a robust regular expression that should get me a clean true or false using testx. 

Your best bet may be to wrap a NX query into the api using the query endpoint and query parameter, and see if that works. eg select YourTable[testx(concat(CAE), "\b11029\b")], url-encoded and appended to the below url structure. 

https://api.ninoxdb.de/v1/teams/:teamid/databases/:databaseid/query?query=

from the API manual:

Execute a Ninox Script

With the following request you can execute any valid Ninox script against a database.

Few things to consider -

The output of the script will be streamed back as the response.
Scripts having any compilation errors will terminate the request with a null reponse.
Request

The request can be executed using both GETand POST HTTP methods

GET https://api.ninoxdb.de/v1/teams/:teamid/databases/:databaseid/query?query=1+2

There's also the contains() function which may be simpler than testx()