The VE 10-35 X is only listed on this page of the Victor-Victrola page --
http://www.victor-victrola.com/Production%20Volumes.htm New data is added all the time, so check back there from time to time.
In any event, here's the information from "Look for the Dog," by Robert Baumbach, 1994 ed. -- P. 210
Ten-Thirty-Five" Introduced 1928; Original Price -- $365.00
"The 1928 Automatic Orthophonic Victrola 10-35 used the second style of automatic changer designed by Victor, which was somewhat simpler and less expensive than the original changer introduced nearly two years earlier. The cabinet was also simpler in construction and smaller in size than that of the original Automatic Orthophonic, the 10-50, with the result that the price of this machine was nearly half that of the older model.
This was the least expensive instrument with an automatic record changer ever made by the Victor Talking Machine Co. There were no options with this Victrola--you liked the walnut cabinet and electric motor (the universal motor was available on special order for $20 extra) or chose a different phonograph. Standard, too, were all the expected deluxe Victor Orthophonic features such as the non set automatic brake, speed adjuster, ten inch turntable, with antique brass finish, and four special record albums--all were 12 inches high, but two were fitted with 10-inch sleeves. The cabinet was 40.5 inches high, 34.75 inches wide, and 20 inches deep."
As noted in Robert Baumbach's Victor Data Book, this was fitted with the large metal re-entrant horn. (It measures six feet in length, according to some collectors, and is identical to the one installed in the 8-35, 9-8 and 9-9.) The book also states that only 3,082 were shipped between the third quarter of 1928 and the fourth quarter of 1930. (RCA acquired Victor in 1929.) The 1931 RCA Victor replacement parts list indicates that the final serial number was 11177. (There is a gap in serial numbers due to recalled record changers)
As for current value, it would probably be close to a 10-50, or about $2,000+++ depending on condition; perhaps more since it is comparatively rare. To be frank, I've never seen a
complete 10-35 come up for sale on ebay, or anywhere. (There was an empty cabinet model on Craigslist, awhile back, and I believe that the seller wanted about $300 for it.)
If at all possible, could you please post some photos of this, especially the changing mechanism, and front of cabinet, with the doors closed as well as open (to show the grille.)