Request API search based on ticket custom fields date range

I'm developing an application that allows users to select dates and insert them into custom fields. My goal is to utilize the Zendesk API to search for tickets based on specific start and end dates, which are represented as custom fields within the tickets. Here's an example of the URL I'm trying for the search query:

https://<domain>.zendesk.com/api/v2/search.json?query=type:ticket custom_field_16896528598683>=2024-04-21 custom_field_16896502734363<=2024-04-25

In this URL, custom_field_16896528598683 represents the start date and custom_field_16896502734363 represents the end date. My objective is to find tickets that either overlap or fall within the specified date range. The purpose of this search is to prevent the assignment of dates to a new ticket if another ticket already includes those dates, ensuring date uniqueness across tickets.
Is it possible to do? Or I need to search all tickets and pass one by one?