SELECT 
  category_id 
FROM 
  q_categories 
WHERE 
  id_path LIKE '2/11/%'

Query time 0.00039

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "12.21"
    },
    "table": {
      "table_name": "q_categories",
      "access_type": "range",
      "possible_keys": [
        "id_path"
      ],
      "key": "id_path",
      "used_key_parts": [
        "id_path"
      ],
      "key_length": "767",
      "rows_examined_per_scan": 8,
      "rows_produced_per_join": 8,
      "filtered": "100.00",
      "index_condition": "(`portal`.`q_categories`.`id_path` like '2/11/%')",
      "cost_info": {
        "read_cost": "10.61",
        "eval_cost": "1.60",
        "prefix_cost": "12.21",
        "data_read_per_join": "21K"
      },
      "used_columns": [
        "category_id",
        "id_path"
      ]
    }
  }
}