Clustering points in PostGIS

I'd suggest to use the ST_ClusterDBSCAN Window function rather than the Aggregate function ST_ClusterWithin:

SELECT *,
       ST_ClusterDBSCAN(the_geom, eps := <distance>, minpoints := 1) OVER() AS clst_id
FROM   all_locations
;

clst_id will hold INT values representing the cluster each rows geometry belongs to.

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As stated in the comments, ST_ClusterWithin will aggregate geometries that are separated by no more than the distance to each other; using minpoints := 1 in ST_ClusterDBSCAN will force the same effect.

Compare

WITH
    pts AS (
        SELECT  ST_MakePoint(n, 0) As geom
        FROM    Generate_Series(0, 5) AS n
    )

SELECT  dmp.clst_id
FROM    (
    SELECT  ST_ClusterWithin(geom, 1) AS cw
    FROM    pts
) AS    clst,
        UNNEST(clst.cw) WITH ORDINALITY AS dmp (clst, clst_id),
        LATERAL ST_Dump(ST_CollectionExtract(dmp.clst, 1)) AS extr
;


 clst_id |    geom    
---------+------------
       1 | POINT(0 0)
       1 | POINT(1 0)
       1 | POINT(2 0)
       1 | POINT(3 0)
       1 | POINT(4 0)
       1 | POINT(5 0)
(6 rows)

to

WITH
    pts AS (
        SELECT  ST_MakePoint(n, 0) As geom
        FROM    Generate_Series(0, 5) AS n
    )

SELECT ST_ClusterDBSCAN(geom, 1, 1) OVER() AS clst_id,
       ST_AsText(geom) AS geom
FROM   pts
;


 clst_id |    geom    
--------+------------
      0 | POINT(0 0)
      0 | POINT(1 0)
      0 | POINT(2 0)
      0 | POINT(3 0)
      0 | POINT(4 0)
      0 | POINT(5 0)
(6 rows)

In both cases the geometries are stretched over a total distance of 5 degrees, but count as one and the same cluster (ST_ClusterDBSCAN starts counting at 0, whereas the ORDINALITY stars at 1) since they are within distance/eps of 1 degree to each other!

This behavior may change for minpoints > 1 (and on other data than the above), as there need to be at least minpoints core geometries within eps distance to get counted as cluster.

Needless to say, the latter approach is way less convoluted, and offers some nice functionality built into the windowing behavior (e.g. easy clustering over attributes etc.)

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Note:

Both functions assume distance/eps in units of the underlying CRS; for a geographic reference system, this is degrees! Since there is no signature accepting GEOGRAPHY for neither of them, you will need to ST_Transform your data into a suitable projection to be able to work with metric/imperial units.