Custom cache key - cookie : purge cache by url

Our Cloudflare cache has a custom cache key which has a cookie. When I use CURL to purge cache by url with the cookie name and value, the cache is not purged for the URL which has the cookie.

Here is the purge by url CURL Call
curl -X POST “” -H “X-Auth-Email: [email protected]” -H “X-Auth-Key:dd293792454545454547c4f67445479de3943bh3h3432” -H “Authorization: Bearer ddfd434355_25CsqSgKD3adfdfdfdfdJZdfefSdfddddd1DX9wn” -H “Content-Type: application/json” --data ‘{“files”:[“url”],“cookie”:"[loggedin=1]"}’

The API response is a success, but the cache is not purged. is my CURL API call for “purge by URL” is correct? If my Cloudflare custom cache key using a cookie and query params, what should be my API call syntax? is my above purge by URL API call correct?