What possibly disease if the tubes connecting to your balls is bigger than the other side?

Spermaticcord inflam: I assume that you are refering to the spermatic cord which is is a collection of strcutres starting at the back of testes and ascending up through the base of scrotum , through the groin to enter the abdomen and end up as vasdeferens , one on either side which unites with seminal vesicle and open in the back of prostate gland into the prost.Urethra .It could be a normal variation /inflammed.See doc.

Few: Epididimitis, syphillis. Gonorrhea. Tb. Varicocele. Epididimal cyst.

Several things.: A painless enlargement in the area of the cables which connect your testicles to your abdomen is very likely a benign condition known as hydrocele, varicocele or spermatocele. The hydrocele sometimes feels like a sausage or tubular structure while the varicocele often feels like a bag of worms. Spermatoceles can often be felt on top of the testicle like a cyst. Sometimes these cause discomfort.