Firstly, the stock price might increase on the date when a firm make a announcemen to the public if investors view cash dividend as good news. The stock price rised from 10 to 11 and the cash dividend is 1, personally, this is coincident.
Secondly, the stock price will drop by the amount of cash dividend on the ex-dividend date because one day before the ex-dividend day, owners of the shares are entitled to obtain cash dividend, while on ex-dividend day, owners are not entitled to obtain cash dividend. So the difference between these two days should be the cash dividend theoretically (if we ignore other factors, such as taxes)
Hopefully it is useful!