Mysterious Taker

Went fishing in the keys Memorial Weekend. Stayed in Marathon and brought along one rod, while fishing for two nights. I had two really mysterious situations. The first night I had a Jack for bait and paddled the bait out about 200 yds at approx. 6:30 PM along with a cinderblock tied to it. I waited an hour and the line started come out slowly in spurts. After about 10 minutes of this, the line shot out quickly and I decided to reel it in. As I started to reel it in, the line was really tight and felt like I was reeling in the dead weight of a boat. I didn't feel any head shakes or change of direction. I made very little progress and probably still had 100 yards left to reel in. So, I decided to tie the line off and get it in the morning. Woke up the next morning and I take my kayak out to retrieve the line. As I get within 20 yds of the end of the line, I try to pull it in and it is so tight and has a lot of tension, it snapped. I was a little timid as I'm not a frequent shark fisherman, so I didn't want to dive and see what it was. The second night I had a very similar situation. I paddled out a snapper carcass at the same time, 6:30 PM along with a cinderblock tied to it. About two hours later, the line came out slowly again in spurts. I waited about 30-45 minutes and it kept coming out slowly in spurts. I decided to reel it in and gained back around 50 yds of line and it just went slack and the line was cut. First off, has anyone had similar experiences like this and know what it could have been the first night? Also are there any ways I can improve my hookups, because I don't know why the line came out slowly rather than quick, long runs.

Thanks, Alex